Strong Charge-Photon Coupling in Planar Germanium Enabled by Granular Aluminium Superinductors

High kinetic inductance superconductors are gaining increasing interest for the realisation of qubits, amplifiers and detectors. Moreover, thanks to their high impedance, quantum buses made of such materials enable large zero-point fluctuations of the voltage, boosting the coupling rates to spin and charge qubits. However, fully exploiting the potential of disordered or granular superconductors is challenging, as their inductance and, therefore, impedance at high values are difficult to control. Here we have integrated a granular aluminium resonator, having a characteristic impedance exceeding the resistance quantum, with a germanium double quantum dot and demonstrate strong charge-photon coupling with a rate of $g_\text{c}/2π= (566 \pm 2)$ MHz. This was achieved due to the realisation of a wireless ohmmeter, which allows \emph{in situ} measurements during film deposition and, therefore, control of the kinetic inductance of granular aluminium films. Reproducible fabrication of circuits with impedances (inductances) exceeding 13 k$Ω$ (1 nH per square) is now possible. This broadly applicable method opens the path for novel qubits and high-fidelity, long-distance two-qubit gates.

💡 Research Summary

This paper reports the design, fabrication, and demonstration of a high‑impedance superconducting resonator based on granular aluminum (grAl) that achieves strong charge‑photon coupling to a planar germanium double‑quantum‑dot (DQD) device. High kinetic‑inductance superconductors are attractive for quantum circuits because their large characteristic impedance (Z) amplifies zero‑point voltage fluctuations, thereby increasing the coupling strength g_c ∝ √Z between microwave photons and charge or spin qubits. However, disordered superconductors such as grAl suffer from poor reproducibility of their sheet resistance (R_s), which directly determines kinetic inductance (L_k) and thus Z.

To overcome this, the authors develop a vacuum‑compatible wireless ohmmeter equipped with an independently rotatable shutter. The system allows in‑situ two‑probe resistance measurements of test samples placed in four quadrants of the deposition holder. By iteratively adjusting the oxygen flow during electron‑beam evaporation of Al, they terminate the deposition precisely when the target R_s (≈2.5 kΩ/□) is reached. This feedback reduces the standard deviation of R_s from ~2.3 kΩ (without feedback) to <0.8 kΩ and also narrows the thickness distribution, enabling reliable fabrication of grAl films with kinetic inductances up to L_k = 2.7 ± 0.1 nH/□.

Using these films, the team fabricates λ/2 coplanar waveguide (CPW) resonators with center‑conductor widths ranging from 10 µm down to 100 nm. The impedance scales as Z ≈ √(L_k/w), so narrowing the line dramatically raises Z. Measured characteristic impedances span from 9 kΩ for 200 nm wide lines to a record 22.3 ± 0.3 kΩ for 100 nm lines, while maintaining internal quality factors Q_i > 10⁴ even in the single‑photon regime. The narrow conductors also improve magnetic‑field resilience: out‑of‑plane fields up to B⊥ ≈ 281 mT and in‑plane fields up to B∥ ≈ 3.5 T are tolerated before the internal Q degrades, a crucial property for spin‑qubit platforms that require sizable magnetic fields.

The high‑impedance resonator (Z ≈ 7.9 kΩ, L_k ≈ 800 pH/□) is then integrated with a Ge/SiGe heterostructure DQD hosting hole spins. The device is measured in a reflection geometry to enhance signal‑to‑noise. By tuning the interdot detuning ε, the charge transition of the DQD is brought into resonance with the microwave mode at 7.262 GHz. A clear vacuum‑Rabi splitting is observed, and fitting yields a charge‑photon coupling rate g_c/2π = 566 ± 2 MHz. The resonator decay rate κ/2π is ≈1.5 MHz and the charge decoherence rate γ/2π ≈0.8 MHz, satisfying the strong‑coupling condition g_c ≫ κ, γ. The cooperativity C = g_c²/(κγ) reaches 251 ± 8, surpassing previous semiconductor cQED implementations (typically C < 100).

These results demonstrate that granular‑aluminum superinductors, when fabricated with precise in‑situ resistance monitoring, can reliably provide impedances well above the resistance quantum (R_Q ≈ 6.5 kΩ). The combination of high Z, low loss, and robust magnetic‑field tolerance makes them ideal candidates for mediating long‑distance interactions between spin qubits. In particular, the strong charge‑photon coupling achieved here can be leveraged to enhance spin‑photon coupling via spin‑orbit interaction in germanium hole systems, paving the way for high‑fidelity, long‑range two‑qubit gates.

Beyond the specific Ge DQD platform, the wireless‑ohmmeter technique is transferable to other disordered superconductors (e.g., TiN, NbTiN), enabling scalable production of superinductors for a variety of quantum technologies, including fluxonium qubits, kinetic‑inductance parametric amplifiers, and photon‑mediated quantum networks. The work thus provides a practical roadmap for integrating ultra‑high‑impedance superconducting circuitry with semiconductor quantum dots, addressing a key bottleneck in the development of scalable quantum processors.